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在抽样调查中,经常会遇到研究变量与其相关的辅助变量之间呈现非线性关系的情形,这时应用传统的广义回归估计方法将存在较大的局限和不足。为了解决这一问题,本文首先假定超总体模型的回归函数为一般形式的光滑函数,从而构建出半参数回归模型,利用半参数乘积调整方法对模型进行拟合,结合广义差分估计原理提出一种新型的半参数模型辅助抽样估计量,通过理论证明和数值模拟分析分别对比验证了这一套估计方法与传统方法相比所具备的有效性。在此基础上,对于在我国社会经济统计中如何应用这一套估计方法进行了展望。
In the sample survey, we often encounter the non-linear relationship between the research variables and its related auxiliary variables. At this time, the application of the traditional generalized regression estimation method will have greater limitations and deficiencies. In order to solve this problem, we first assume that the regression function of the super-total model is a smooth function of the general form, so as to construct a semi-parametric regression model and use the semi-parametric product adjustment method to fit the model. Based on the principle of generalized difference estimation, The new semiparametric model aided sampling estimator, compared with the traditional method through the proof of theory and numerical simulation respectively verify the effectiveness of this set of estimation methods compared with the traditional method. On this basis, the paper forecasts how to apply this set of estimation methods in China’s socio-economic statistics.